%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC009+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:07:29 PM UTC 2026
% Result : Theorem 0.68s 1.07s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 33 ( 18 unt; 0 def)
% Number of atoms : 167 ( 67 equ)
% Maximal formula atoms : 23 ( 5 avg)
% Number of connectives : 213 ( 79 ~; 68 |; 55 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 46 !; 24 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X2
& nil != X3 )
| ! [X7] :
( ssList(X7)
=> ( ? [X8] :
( ? [X9] :
( ? [X10] :
( ? [X11] :
( lt(X10,X8)
& app(X11,cons(X10,nil)) = X2
& ssList(X11) )
& ssItem(X10) )
& app(cons(X8,nil),X9) = X7
& ssList(X9) )
& ssItem(X8) )
| ~ strictorderedP(X2)
| app(X2,X7) != X3 ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( app(X4,X6) = X0
& app(app(X4,X5),X6) = X1
& ssList(X6) )
& ssList(X5) )
& ssList(X4) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X2
& nil != X3 )
| ! [X7] :
( ssList(X7)
=> ( ? [X8] :
( ? [X9] :
( ? [X10] :
( ? [X11] :
( lt(X10,X8)
& app(X11,cons(X10,nil)) = X2
& ssList(X11) )
& ssItem(X10) )
& app(cons(X8,nil),X9) = X7
& ssList(X9) )
& ssItem(X8) )
| ~ strictorderedP(X2)
| app(X2,X7) != X3 ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( app(X4,X6) = X0
& app(app(X4,X5),X6) = X1
& ssList(X6) )
& ssList(X5) )
& ssList(X4) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( nil != X2
| nil = X3 )
& ? [X7] :
( ssList(X7)
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ! [X11] :
( ~ lt(X10,X8)
| app(X11,cons(X10,nil)) != X2
| ~ ssList(X11) )
| ~ ssItem(X10) )
| app(cons(X8,nil),X9) != X7
| ~ ssList(X9) )
| ~ ssItem(X8) )
& strictorderedP(X2)
& app(X2,X7) = X3 )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( app(X4,X6) != X0
| app(app(X4,X5),X6) != X1
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssList(X4) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( nil != X2
| nil = X3 )
& ? [X7] :
( ssList(X7)
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ! [X11] :
( ~ lt(X10,X8)
| app(X11,cons(X10,nil)) != X2
| ~ ssList(X11) )
| ~ ssItem(X10) )
| app(cons(X8,nil),X9) != X7
| ~ ssList(X9) )
| ~ ssItem(X8) )
& strictorderedP(X2)
& app(X2,X7) = X3 )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( app(X4,X6) != X0
| app(app(X4,X5),X6) != X1
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssList(X4) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f109,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(ennf_transformation,[],[f84]) ).
fof(f155,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ( nil != sK2
| nil = sK3 )
& ssList(sK4)
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ! [X11] :
( ~ lt(X10,X8)
| app(X11,cons(X10,nil)) != sK2
| ~ ssList(X11) )
| ~ ssItem(X10) )
| app(cons(X8,nil),X9) != sK4
| ~ ssList(X9) )
| ~ ssItem(X8) )
& strictorderedP(sK2)
& sK3 = app(sK2,sK4)
& ! [X4] :
( ! [X5] :
( ! [X6] :
( app(X4,X6) != sK0
| app(app(X4,X5),X6) != sK1
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssList(X4) )
& sK0 = sK2
& sK1 = sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X7,sK4)],[f99]) ).
fof(f169,plain,
ssList(sK0),
inference(cnf_transformation,[],[f155]) ).
fof(f170,plain,
ssList(sK1),
inference(cnf_transformation,[],[f155]) ).
fof(f174,plain,
ssList(sK4),
inference(cnf_transformation,[],[f155]) ).
fof(f177,plain,
sK3 = app(sK2,sK4),
inference(cnf_transformation,[],[f155]) ).
fof(f178,plain,
! [X6,X4,X5] :
( app(X4,X6) != sK0
| app(app(X4,X5),X6) != sK1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f155]) ).
fof(f179,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f155]) ).
fof(f180,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f155]) ).
fof(f194,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f109]) ).
fof(f203,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f242,plain,
! [X6,X4,X5] :
( app(X4,X6) != sK2
| app(app(X4,X5),X6) != sK3
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(definition_unfolding,[],[f178,f180,f179]) ).
fof(f243,plain,
ssList(sK3),
inference(definition_unfolding,[],[f170,f180]) ).
fof(f244,plain,
ssList(sK2),
inference(definition_unfolding,[],[f169,f179]) ).
tcf(c_49,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X2) != sK2 )
| ( app(app(X0,X1),X2) != sK3 ) ),
inference(cnf_transformation,[],[f242]) ).
tcf(c_50,negated_conjecture,
app(sK2,sK4) = sK3,
inference(cnf_transformation,[],[f177]) ).
tcf(c_53,negated_conjecture,
ssList(sK4),
inference(cnf_transformation,[],[f174]) ).
tcf(c_57,negated_conjecture,
ssList(sK3),
inference(cnf_transformation,[],[f243]) ).
tcf(c_58,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f244]) ).
tcf(c_72,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f194]) ).
tcf(c_81,plain,
ssList(nil),
inference(cnf_transformation,[],[f203]) ).
tcf(c_2909,plain,
! [X0: $i] :
( ~ ssList(sK4)
| ~ ssList(sK2)
| ~ ssList(X0)
| ( app(sK2,X0) != sK2 )
| ( app(sK3,X0) != sK3 ) ),
inference(superposition,[status(thm)],[c_50,c_49]) ).
tcf(c_2910,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( app(sK2,X0) != sK2 )
| ( app(sK3,X0) != sK3 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2909,c_53,c_58]) ).
tcf(c_2914,plain,
( ~ ssList(nil)
| ( app(sK2,nil) != sK2 )
| ( app(sK3,nil) != sK3 ) ),
inference(instantiation,[status(thm)],[c_2910]) ).
tcf(c_3040,plain,
app(sK3,nil) = sK3,
inference(superposition,[status(thm)],[c_57,c_72]) ).
tcf(c_3041,plain,
app(sK2,nil) = sK2,
inference(superposition,[status(thm)],[c_58,c_72]) ).
tcf(c_3055,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3040,c_3041,c_2914,c_81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC009+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.34 % Computer : n011.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 15:53:15 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.38 Running first-order theorem proving
% 0.13/0.39 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 0.68/1.07 % SZS status Started for theBenchmark.p
% 0.68/1.07 % SZS status Theorem for theBenchmark.p
% 0.68/1.07
% 0.68/1.07 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.68/1.07
% 0.68/1.07 % ------ iProver source info
% 0.68/1.07
% 0.68/1.07 % git: date: 2026-07-19 20:42:38 +0200
% 0.68/1.07 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.68/1.07 % git: non_committed_changes: false
% 0.68/1.07
% 0.68/1.07 % ------ Parsing...
% 0.68/1.07 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.68/1.07
% 0.68/1.07 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.68/1.07
% 0.68/1.07 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.68/1.07
% 0.68/1.07 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.68/1.07 % ------ Proving...
% 0.68/1.07 % ------ Problem Properties
% 0.68/1.07
% 0.68/1.07 %
% 0.68/1.07 % clauses 65
% 0.68/1.07 % conjectures 8
% 0.68/1.07 % EPR 19
% 0.68/1.07 % Horn 42
% 0.68/1.07 % unary 11
% 0.68/1.07 % binary 6
% 0.68/1.07 % lits 220
% 0.68/1.07 % lits eq 59
% 0.68/1.07 % fd_pure 0
% 0.68/1.07 % fd_pseudo 0
% 0.68/1.07 % fd_cond 15
% 0.68/1.07 % fd_pseudo_cond 7
% 0.68/1.07 % AC symbols 0
% 0.68/1.07
% 0.68/1.07 % ------ Schedule dynamic 5 is on
% 0.68/1.07
% 0.68/1.07 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.68/1.07
% 0.68/1.07
% 0.68/1.07 % ------
% 0.68/1.07 % Current options:
% 0.68/1.07 % ------
% 0.68/1.07
% 0.68/1.07
% 0.68/1.07 %
% 0.68/1.07
% 0.68/1.07 % ------ Proving...
% 0.68/1.07 %
% 0.68/1.07
% 0.68/1.07 % SZS status Theorem for theBenchmark.p
% 0.68/1.07
% 0.68/1.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.68/1.07
% 0.68/1.07
%------------------------------------------------------------------------------